Pat the chicken breasts dry with paper towels. If they are very thick, slice them horizontally or pound them to an even thickness. Season both sides with garlic powder, onion powder, paprika, salt, and black pepper.
Heat the olive oil and butter in a large oven-safe skillet over medium-high heat. Sear the chicken for 3–4 minutes per side until golden brown. The chicken does not need to be fully cooked yet. Transfer the chicken to a plate and set aside.
Reduce the heat to medium-low. Add the minced garlic to the skillet and sauté for 30 seconds until fragrant. Sprinkle in the flour and stir for 1 minute. Gradually whisk in the chicken broth until smooth.
Remove the skillet from the heat and let it cool slightly. Whisk in the sour cream, Dijon mustard, and Italian seasoning until creamy.
Preheat the oven to 375°F. Return the chicken to the skillet and spoon the sour cream sauce over each piece. Sprinkle the mozzarella and Parmesan cheese evenly over the top.
Transfer the skillet to the oven and bake for 15–20 minutes, depending on the thickness of the chicken, until the cheese is melted and bubbling and the chicken reaches an internal temperature of 165°F. If your skillet is not oven-safe, transfer the chicken and sauce to a greased baking dish before baking.
Remove from the oven and let the chicken rest for 5 minutes. Sprinkle with fresh parsley and spoon extra creamy sauce over each serving.
Notes
Ensure the chicken is cooked to an internal temperature of 165°F for safety.
Feel free to add vegetables like spinach or mushrooms to the sauce for added flavor.